New matrices for spectral hypergraph theory, I
Combinatorics
2024-11-12 v1
Abstract
We introduce a hypergraph matrix, named the unified matrix, and use it to represent the hypergraph as a graph. We show that the unified matrix of a hypergraph is identical to the adjacency matrix of the associated graph. This enables us to use the spectrum of the unified matrix of a hypergraph as a tool to connect the structural properties of the hypergraph with those of the associated graph. Additionally, we introduce certain hypergraph structures and invariants during this process, and relate them to the eigenvalues of the unified matrix.
Cite
@article{arxiv.2411.07214,
title = {New matrices for spectral hypergraph theory, I},
author = {R. Vishnupriya and R. Rajkumar},
journal= {arXiv preprint arXiv:2411.07214},
year = {2024}
}
Comments
32 pages, 6 figures